Question

Nine similar resistors of resistance R are connected as shown in the figure. Equivalent resistance between points A and B is:

• A. $3R/5$
• B. $4R/3$
• C. $9R/5$
• D. $R$

Answer 1

The correct option is A $3R/5$

Potential drop after $R_2$ and $R_3$ is same,

i.e $V_P=V_Q⟹$ There will be no current through $R_3⟹$ We can neglect $R_3$

Similarly, Potential drop after $R_5$ and $R_4$ is same,

i.e $V_R=V_S⟹$ There will be no current through arm $R_S\left(R_g\right)⟹$ We can neglect $R_g$.

$\therefore$ after neglecting $R_3$ and $R_g$ ,

$(R_2,R_5,R_7),(R_1,R_4,R_9)$These set are series and they in parallel with $R_6$.

$⟹\frac{1}{R_{eq}}=\frac{1}{3R}+\frac{1}{3R}+\frac{1}{R}=\frac{5}{3R}$

$R_{eq}=\frac{3R}{5}\Omega$